If Y is dependent variable and X is Independent variable and the S.D of X andY are 5 and 8 respectively and Co-efficient of co-relation between X and Y is0.8. Find the Regression co-efficient of Y on X.(a) 0.78(b) 1.28(c) 6.8(d) 0.32
Question
If Y is dependent variable and X is Independent variable and the S.D of X andY are 5 and 8 respectively and Co-efficient of co-relation between X and Y is0.8. Find the Regression co-efficient of Y on X.(a) 0.78(b) 1.28(c) 6.8(d) 0.32
Solution
The regression coefficient of Y on X, also known as the slope of the regression line, can be calculated using the formula:
b = r * (Sy/Sx)
where:
- r is the correlation coefficient between X and Y,
- Sy is the standard deviation of Y, and
- Sx is the standard deviation of X.
Given in the problem:
- r = 0.8,
- Sy = 8, and
- Sx = 5.
Substituting these values into the formula gives:
b = 0.8 * (8/5) = 1.28
So, the regression coefficient of Y on X is 1.28. Therefore, the correct answer is (b) 1.28.
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